Answer: The side of the original square is 4 feet.
Step-by-step explanation:
Given , the sides of the original square is lengthened by 7 feet.
The area of the new square = 121 square feet.
Let the original side of square be<em> 'x'.</em>
The new side = <em>x+7</em>
Area of new square =(side)² = <em>(x+7)²</em>
As per given , we have

![\Rightarrow\ (x+7)^2=11^2\ \ \ [\because\ 11^2=121]](https://tex.z-dn.net/?f=%5CRightarrow%5C%20%28x%2B7%29%5E2%3D11%5E2%5C%20%5C%20%5C%20%5B%5Cbecause%5C%2011%5E2%3D121%5D)
Taking square roots on both sides , we get

Hence, the side of the original square is 4 feet.